Understanding the change of flux and it's consequences

[Pyrus96]

So I was busy trying to imagine the ways in which lenz's Law would work physically. So I imagined a loop through which a magnet is brought and after that the magnet is pulled out of the loop a current is induced in order to keep up the magnetic field. So in this case the flux would go down which in turn would produce a positive emf and in its turn a current. Put as I was trying to imagine something struck me odd, why would particles start moving? A mere change of magnetic field is not enough to make a particle move because in order for a particle to move it has to has to have a force moving it and the magnetic force isn't the cause because it never does work so why does a current starts

 

[nasu]

The variable magnetic field produces an electric field.